A-level Mathematics/OCR/C1/Equations/Solutions

Manipulating Equations

Collecting Like Terms

1. $2x$
2. $4x^{2}$
3. $3x^{3}+5x$
4. $3zy+2y+2z$
5. $-x^{2}+4x^{2}y-4xy^{2}+7xy$

Multiplication

1. $4x^{2}$
2. $18x^{2}y^{2}$
3. $36ab^{2}xz$
4. $60x^{5}y^{4}z^{2}$
5. ${\sqrt {x^{5}}}$

Fractions

1. $x$
2. ${\frac {7x}{12}}$
3. ${\frac {16xy}{15}}$
4. $2x-y+z$
5. ${\frac {x^{2}+y^{2}}{xy}}$

Solving Equations

Changing the Subject of an Equation

1. Solve for x.

$x={\frac {y}{2}}$

1. Solve for z.

$z={\frac {x-8}{3}}$

1. Solve for y.

$y=b^{2}$

1. Solve for x.

$x={\sqrt {y+9}}$

1. Solve for b.

$b={\frac {6y+7z}{6}}$

Solving Quadratic Equations

Find the Roots of:

1. $x=-2\ or\ 3$
2. $x=7\ or\ {\frac {3}{2}}$
3. $x=2\ or\ 3$
4. $x=-1\ or\ 0$
5. $x=-3\ or\ 4$

Simultaneous Equations

1. $a=4,s=2$
2. $c={\frac {2}{5}},d=1$
3. $b=7,g=12$